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[0000-A] Signals and Systems Using MATLAB an Effective Application for Exploring and Teaching Media Signal Processing

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  Signals and Systems Using MATLAB: An Effective Application forExploring and Teaching Media Signal Processing Bob L. Sturm and Jerry GibsonGraduate Program in Media Arts & Technology (MAT)University of California, Santa Barbara { b.sturm, gibson } @mat.ucsb.edu Abstract  A problem exists in many digital media arts programs of howto effectively teach students with little mathematical practicethe principles of media signal processing. Blackboard lec-tures and elementary engineering textbooks lead to conster-nation and apathy; the course becomes more of a math classthan anything else. This robs the student of a unique oppor-tunity to learn, apply, and explore digital media processing— an inherently multimedia field. We have created a large set of exploratory demonstrations and applications programmed in MATLAB to entice and inspire students who do not yet pos-sess the mathematical knowledge necessary for thorough re-search in media signal processing. Our application, “Signalsand Systems Using MATLAB,” can be used to supplement anycourse concerned with these topics. It can be obtained for  free from  http://www.mat.ucsb.edu/SSUM  . 1 Introduction There is no doubt that learning media signal processingshould be a required portion of any new media arts program;students should at least understand the algorithms behind thesoftware they use, the specifications of their hardware, andbe able to effectively communicate with engineers. But howbeneficial is it to just teach this type of student to add sinewaves in the complex domain, convolve two signals on paper,and prove the convergence of a series? As expected many stu-dents develop consternation and apathy, and quickly learn theminimum motions necessary to slide by. Instead of findingcreative applications for the concepts they are learning, stu-dent might spend most of their time working on elementaryproblems, such as adding phasors. By the end a student maybe able to do convolution on paper, but has little knowledgeof how it can, or even why it should, be applied.There are three things working against a successful syl-labus for teaching media signal processing to new media stu-dents. First, the amount of mathematics required to do any-thing interesting is much higher than what most artists arecomfortable with. The course might then become more con-cerned with complex mathematics and trigonometry than me-dia signal processing. Second, the pace of the course couldbe set back by the need to address the mathematics. After tenweeks the interesting topics might still be weeks away. Fi-nally, since media signal processing includes both sound andimage, the number of topics that can be addressed more thandoubles. If among the pursuits of digital media arts programsis to imbue artists with practical engineering knowledge, thena more effective and ultimately useful presentation of mediasignal processing needs to be employed.There is a large number of published texts that deal withmultimediaand media signal processing (McClellan, Schafer,and Yoder 1998, 2003; Steiglitz 1996). Most of these textshowever are either too advanced for someone with little mathknowledge, or too general.  DSP First: A Multimedia Ap- proach  (McClellan, Schafer, and Yoder 1998) is perhaps theeasiest text, and attempts to make the material more accessi-ble by including a CD-ROM that has tutorials, movies, andMATLAB demonstrations. However, the CD-ROM contentsare not of much pedagogical use or interest to new media stu-dents; the five MATLAB demonstrations included are unin-teresting and uninspiring.Searching through the world wide web one can find aneven larger amount of material aiming to make media sig-nal processing accessible. Clausen and Spanias (1998) de-scribe the use of an on-line digital signal processing (DSP)laboratory using Java to present visualizations and interac-tive demonstrations. Rahkila and Karjalainen (1998) describethe benefit of computer-based education for teaching DSPby virtue of it being multimedia. Illustrating complex func-tions like filtering by actually applying it to a sound createsa longer-lasting impression than just deriving its frequencyresponse on paper. Joaquim, Pereira, and de Oliveira (1998)describe an engineering course based on MATLAB to pro-vide “a fast and natural way to DSP concepts and practicalapplications;” almost immediately students can be creating  and understanding their own DSP algorithms. It is clear thatsince many students in digital media arts programs are uniqueand individual—visual artists, sound composers and design-ers, and multimedia engineers—what is required is “hand-crafted course-ware” (Hague 1997) that addresses the multi-media nature of media signal processing, as well as the cre-ative motivation of these students.To circumvent the difficulties outlined above, we havecreated a collection of exploratory applications designed tomotivate and inspire students to learn and apply concepts of media signal processing. By speaking to their artistic inter-ests and showing the usefulness of the theory the studentswill accept the learning curve and be more likely to applythemselves. 2 SSUM: Signals and Systems UsingMATLAB SSUM is an application containing many demonstrationsandexploratoryapplicationsprogrammedinMATLAB.Theseapplications are designed specifically to entice and inspirestudents who do not yet possess the mathematical knowledgenecessary for thorough research in media signal processing.To use SSUM MATLAB must be installed as well as its sig-nal processing toolkit. The cost of this software to the studentis a bit more than a good engineering text, but it is hoped thatafter becoming acquainted with the power of MATLAB, thestudent will continue to use it to explore algorithms, work with data, and apply it to their creative work  1 .SSUM demonstrates essential principles and concepts of media signal processing without requiring rigorous mathe-matics; exploration and learning is done first using softwarerather than paper. SSUM currently has over 20 exploratoryapplications demonstrating properties of sine waves, wave-forms, modulation, sampling, aliasing, spectra, filtering, pole-zerodiagrams, convolution, analysisandsynthesis, andstatis-tical signal features. Many of these are applied to sounds andimages, and a few to video. There are also applications thatdemonstrate interesting topics such as sound cross-synthesis,additive synthesis of birdsong, and sine wave speech synthe-sis. SSUM is perfect for use in lectures, labs, and personalexploration. All the programs in SSUM are wrapped in GUIs,so there is no need for typing commands at the prompt. Manyof the applications are integrated as well. For instance, if oneis creating a waveform in an application, it can be sent to an-other SSUM application for filtering or to see its spectrum.Figure 1 shows the Sampling Explorer application. Thisdemonstrationshowshowcontinuoussignalscanbedigitized. 1 One author (Sturm) has used MATLAB as computer music compositionsoftware for six years. Figure 1: Sampling ExplorerUsing the Sampling Explorer one can investigate the causeand effect of aliasing, the effects of quantization, and how toturn digital signals into analog using sinc interpolation.Figure 2: Waveform ExplorerFigure2showsanapplicationdemonstratingthatanywave-form can be created by adding a number of sine waves. Theuser is able to adjust frequency, amplitude, and phase for fif-teen sine waves, as well as select predefined waveforms likesquare or sawtooth. There are buttons to play and write thesound to a file. Additionally, the user can send this wave-form to either the sonogram or Fourier spectrum applicationto see its spectral representation. This way the student can  begin to understand superposition and spectra. This integra-tion of tools within each application is important for givingthe student several views of the same thing—i.e. waveforms,spectral components, and Fourier decomposition.The Fourier Spectrum Explorer, shown in Figure 3, en-ables one to look at the spectrum of a sound. The user candrag a window across the time-domain representation of asignal and animate the spectrum. Formants in vocal soundscan easily be seen. Changing the size and shape of the anal-ysis window leads to different resolutions, demonstrating thetime-frequency trade-off, and effects of different windows. Asimilar application is the Sonogram Explorer, which presentsthe user with the short-time Fourier transform (STFT). Simi-larly, the Image Spectrum Explorer application allows one tolook at spatial frequencies in images.Figure 3: Fourier Spectrum ExplorerFigure 4 shows the Cross-Synthesis Explorer. This appli-cation allows three different methods for cross-synthesizingsounds: convolutionofthetwosounds, amplitudemodulationof one signal by the other, or linear predictive coding—usingone sound as the model and the other as the source. Studentsreally enjoy this demonstration and begin to realize what con-volution does; suddenly the mystery of digital reverberationdisappears.In addition to these applications, SSUM contains demon-strations of MATLAB programming for making sound, mu-sic, and images. The student can experiment with the  Catas-tochastic Additive Synthesis Composition Machine , to syn-thesize a composition in three parts using various envelopesfor amplitudes and frequencies and several other parameters.By using these applications as models, a student can con-struct her own composition machine using other synthesistechniques, like granular, subtractive, and frequency modu-lation. It is expected that as SSUM is used in the classroom,its repository of demonstrations and applications will growexponentially by incorporating good projects by students.Figure 4: Cross-Synthesis ExplorerSSUM uses and extends the programming style used inthe excellent ”MATLAB Auditory Demonstrations” applica-tion (Cooke, Parker, Brown, and Wrigley 1999). Modular-izing the code and keeping the GUI separate from the func-tionality makes SSUM much more manageable. When a newapplication is desired it is quite easy to copy and reuse thefunctionality. 2.1 Why Use MATLAB? There are a several low-level programming languages thatcan be used to demonstrate the application of DSP, such asC++, Java (Clausen and Spanias 1998), and SuperCollider(McCartney 1996). In addition, there are several high-levelsoftware packages that can be used, such as MATLAB, Math-ematica, or Labview. A good overview of several packagescan be found in Nagrial (2002). The authors chose MAT-LAB because of several reasons: its graphics handling andvisualization capabilities, ease and forgiveness of program-ming, graphical user interface development, platform inde-pendence, ability to import and export sound and image data,and its extensive library of advanced routines. (For an in-depth review of why MATLAB was chosen as required soft-warebyaparticularengineeringdepartmentseeDevens(1999)).By using MATLAB as the basis for the course one is ableto introduce applications first, and thus motivate the studentsto experiment and learn how they work, as well as create ap-plications of their own. (Lee 2000) describes the use of MAT-LAB to “help reconcile the declarative (what is) and impera-tive (how to) points of view on signals and systems.” The useof MATLAB in DSP classes and laboratories is described in(Melton, Finelli, and Rust 1999; Radke and Kulkarni 2000;Rajashekar, IEEE, and Bovik 2000). In addition, because of   therelativeeaseofprogramminginMATLABascomparedtoC++ or Java, a student will have more time to concentrate onalgorithms rather than compiler errors. Students using SSUMshould be encouraged to program their own applications us-ing it as a model. Having working examples at their disposaldemonstrates that interesting and complex applications arepossible. 3 Conclusion SSUM has been integrated into a course teaching digitalmedia processing to art and multimedia engineering studentsin the graduate MAT program. The syllabus is not intended tobe exhaustive, but the students should finish with at least anunderstanding of digital signals (e.g. samples, and sampling),spectra (e.g. frequency plots), conversion between analogueand digital systems (e.g. interpolation), filtering (FIR, IIR, Z-transform), and time-frequency analysis (e.g. FFT). With thisknowledge in place the students are more equipped to partici-pate in the complex technology of digital media, whether theyare creating artworks, programming multimedia, or movingonto more complex topics.It might be stated that by focusing on MATLAB in a syl-labus one is replacing the difficulty of learning mathematicswith programming. Thus the class will become more a classof programming MATLAB than learning digital media pro-cessing. However, due to the multimedia nature of media sig-nal processing, it makes more sense to concentrate on practic-ing building applications to learn the theory rather than plug-gingandchuggingwithabstractmathematics. “Iftheteacherscan create an enduring fascination for the subject-matter, the job’s almost over: the more the students love the subject, theless help they need in their studies” (Koumi 1994).By catering to the creative motivations of the media artsstudent, the difficult concepts of media signal processing canbeapproachedwithenthusiasmratherthandread. UsingSSUMand MATLAB the class can provide a practical experience,rather than a pedantic one. And if in the end a student findsnothing useful in media signal processing, at least he has pro-gramming experience that can lend itself to more advancedprogramming.Inadditiontoitsusefulnessformediaartsprograms, SSUMprovidesanexcellenttoolforintroductoryengineeringcourses.Too often engineers are educated through blackboard tech-niques and don’t get to play with the tools. SSUM can bedownloadedforfreefrom http://www.mat.ucsb.edu/SSUM . 3.1 Acknowledgments The MathWorks, Inc., the makers of MATLAB, has sup-ported this research by providing the authors with full multi-platform licenses to MATLAB. References Clausen, A. and A. Spanias (1998). An internet-based computerlaboratory for dsp courses. In  Proceedings of Frontiers in Ed-ucation .Cooke, M., H.Parker, G.J.Brown, andS.N.Wrigley(1999).Theinteractive auditory demonstrations project. In  EurospeechConference .Devens, P. E. (1999). Matlab & freshman engineering. In  Pro-ceedings of the ASEE Annual Conference & Exposition .Hague, A. C. (1997). Towards deeper learning with hand-craftedcourseware. (Bachelor’s Thesis) University of York, Depart-ment of Computer Science, U.K.Joaquim, M. B., J. C. Pereira, and V. A. de Oliveira (1998).Course on dsp design using matlab. In  Proceedings of Fron-tiers in Education .Koumi, J. (1994).  Designing for Learning—Effectiveness with Efficiency, In Effective Screenwriting for Educational Tele-vision, ed. R. Hoey . ?: Kogan Page Ltd.Lee, E. A. (2000). Designing a relevant lab for introductory sig-nals and systems. In  Proceedings of the First Signal Process-ing Education Workshop .McCartney, J. (1996). Supercollider: A new real-time sound syn-thesis language. In  Proceedings of the International Com- puter Music Conference .McClellan, J. H., R. Schafer, and M. A. Yoder (1998).  DSP First: A Multimedia Approach . New Jersey: Prentice Hall.McClellan, J. H., R. Schafer, and M. A. Yoder (2003).  SignalProcessing First  . New Jersey: Prentice Hall.Melton, D. E., C. J. Finelli, and L. M. Rust (1999). A digital sig-nal processing laboratory with style. In  Proceedings of 29th ASEE/IEEE Frontiers in Education Conference .Nagrial, M. (2002). Education and training in engineering soft-ware and applications. In  International Conference on Engi-neering Education .Radke, R. J. and S. Kulkarni (2000). An integrated matlab suitefor introductory dsp education. In  Proceedings of the First Signal Processing Education Workshop .Rahkila, M. and M. Karjalainen (1998). Considerations of com-puter based education in acoustics and signal processing. In Proceedings of Frontiers in Education .Rajashekar, U., IEEE, and A. C. Bovik (2000). Interactive dspeducation using matlab demos. In  Proceedings of the First Signal Processing Education Workshop .Steiglitz, K. (1996).  A DSP Primer: with Applications to Digital Audio and Computer Music . ?: Addison Wesley.
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